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Real representations of semisimple Lie algebras have Q-forms

Dave Witte
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Abstract

We prove that each real semisimple Lie algebra G has a Q-form, such that every real representation of G can be realized over the rational numbers Q. This was previously proved by M.S.Raghunathan (and rediscovered by P.Eberlein) in the special case where G is compact.

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Dave Witte. 2002-12-18. Real representations of semisimple Lie algebras have Q-forms. https://arxiv.org/abs/math/0205289

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